A categories equivalence of associative bimodules

Year 2024, Volume: 36 Issue: 36, 66 - 72, 12.07.2024

Victor López Solís , Marlennhi Moreno Vıllanueva

https://doi.org/10.24330/ieja.1438742

https://izlik.org/JA83WA45LW

Abstract

In this paper we use the classical Wedderburn's Kronecker Factorization Theorem to prove that category of bimodules over $B$ and the category of bimodules over $M_{n}(B)$ are equivalent, where $B$ is some unital associative algebra. In addition to this, we classify the irreducible bimodules over $M_{n}(F).$

Keywords

Kronecker factorization theorem , bimodule , irreducible bimodule

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